Inaugural Lecture of the IAS Focus Group “High-Performance Computing”

We would like to invite you to the Inaugural Lecture of the IAS Focus Group “High-Performance Computing” featuring an inaugural lecture by the Hans Fischer Senior Fellow Prof. Trygve Markus Hegland.

Date: July 26th, 2010

Time: 14:00–15:30 pm

Location: Hörsaal H.E.009 (EG), Leibniz-Rechenzentrum der Bayerischen Akademie der Wissenschaften, Boltzmannstraße 1, 85748 Garching

Prof. Trygve Markus Hegland - Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra

Title: “Challenges and structure of multidimensional problems“

Abstract:

Most traditional techniques like the finite element method have been derived for two and three-dimensional problems. It is well-known that many of these techniques when generalized to multidimensional problems start to become infeasible for relatively small numbers of dimensions. This observation is well-known in the computational science community under the name "curse of dimension". Even highly parallel and very fast computers will only allow the solution of very low-dimensional problems. Around 20 years ago, Prof. Zenger and his collaborators from the TUM have introduced the sparse grid method which pushes the dimension of feasible problems to over 10.

It is less known that the theoretical framework used in finite elements (based on classical Sobolev spaces) also breaks down in high dimensions. The type of regularity required for sparse grid methods for example is no longer a consequence of simple regularity theory for partial differential equations. The theory of higher dimensional problems uses ideas from statistics like the ANOVA decomposition in addition to lower-dimensional manifolds, dimension-weighted Sobolev spaces, function spaces based on tensor products and the concentration of measure.

In this talk I will illustrate the challenges posed by multi-dimensions with a few examples including interpolation, density estimation and the solution of partial differential equations which arise, for example, in plasma physics and molecular biology. Both computational and theoretical questions will be covered. I will focus on the structure of the problems which admits computational approximation and compare this structure to the regularity structure used in lower dimensions. I will then discuss variants of the sparse grid combination technique which are both adaptive, suitable for parallel implementation and address a potential instability of the original combination technique. These techniques naturally fit in with the multi-core and multi-physics questions and thus into the TUM-IAS Focus Group "HPC - Tackling the Multi-Challenge".

All attendees are cordially invited to join the reception following the lecture.

If you plan to attend or if you have further questions please contact

Dirk Pflüger, Institut für Informatik V, TU München, Boltzmannstr. 3, 85748 Garching, Tel. 089/289-18636, eMail: mailto:pflueged@in.tum.de